Mathematics is a structured network of cognitive abstractions subject to precise laws, originally presented almost entirely in prose text and numerals. This approach was the norm until symbolic representation was invented around the 15th Century. The introduction of the symbolic representation allowed people to understand and grasp the abstract nature of mathematics easier and quicker. Resultantly, symbolic representation grew in popularity in mathematics and the associated fields, eventually becoming the new norm and standard. Over the years, symbolic representation became ingrained in mathematic problems present in education, research, science, and engineering. In fact, symbol representation has been used for so long that people assume that mathematic problems can be presented and solved only with symbols and resultantly cannot discern the difference between the visual interface, i.e. symbols, and mathematics itself. While extremely beneficial for research and application purposes, symbolic representation does hinder many people in understanding and using mathematics. Numerous research studies going back to the early 1990s have shown that, when ordinary people are repeatedly presented with mathematical problems in a (non-symbolic) meaningful real-world or real-world-like environment, they rapidly achieve a high level of proficiency. This implies that the difficulties many people experience in doing mathematics are primarily of a linguistic nature, also known as the symbol barrier, and do not indicate a lack of mathematical thinking capacity.
Modern technology allow for new and novel means for representation of ideas and theories. The present invention is an alternative representation for mathematical equations which eliminates the traditional use of symbols in order to provide an alternative and user-friendly interface for mathematics. More specifically, the present invention is a method of using gears, which can be either physical or virtual, in order to visually represent and solve algebraic equations, thus overcoming the symbol barrier. This alternative approach to representing mathematical problems has significant potential, both for uses in mathematics and for educational purposes.